New Z-cyclic triplewhist frames and triplewhist tournament designs

AbstractTriplewhist tournaments are a specialization of whist tournament designs. The spectrum for triplewhist tournaments on v players is nearly complete. It is now known that triplewhist designs do not exist for v=5,9,12,13 and do exist for all other v≡0,1(mod4) except, possibly, v=17. Much less is known concerning the existence of Z-cyclic triplewhist tournaments. Indeed, there are many open questions related to the existence of Z-cyclic whist designs. A (triple)whist design is said to be Z-cyclic if the players are elements in Zm∪A where m=v, A=∅ when v≡1(mod4) and m=v-1, A={∞} when v≡0(mod4) and it is further required that the rounds also be cyclic in the sense that the rounds can be labelled, say, R1,R2,… in such a way that Rj+1 is obtained by adding +1(modm) to every element in Rj. The production of Z-cyclic triplewhist designs is particularly challenging when m is divisible by any of 5,9,11,13,17. Here we introduce several new triplewhist frames and use them to construct new infinite families of triplewhist designs, many for the case of m being divisible by at least one of 5,9,11,13,17

Further combinatorial constructions for optimal frequency-hopping sequences

AbstractFrequency-hopping multiple-access (FHMA) spread-spectrum communication systems employing multiple frequency shift keying as data modulation technique were investigated by Fuji-Hara, Miao and Mishima [R. Fuji-Hara, Y. Miao, M. Mishima, Optimal frequency hopping sequences: A combinatorial approach, IEEE Trans. Inform. Theory 50 (2004) 2408–2420] from a combinatorial approach, where a correspondence between frequency-hopping (FH) sequences and partition-type cyclic difference packings was established, and several combinatorial constructions were provided for FHMA systems with a single optimal FH sequence. In this paper, by means of this correspondence, we describe more combinatorial constructions for such optimal FH sequences. As a consequence, more new infinite series of optimal FH sequences are obtained

Some constructions of combinatorial designs

The objects of study of this thesis are combinatorial designs. Chapters 2 and 3 deal with various refinements of whist tournament, while Chapters 3 and 4 focus on terraces. Chapter 2 is devoted to the investigation of Z-cyclic ordered triplewhist tournaments on p elements, where p = 5 (mod 8); Z-cyclic ordered triplewhist and directed triplewhist tournaments on p elements, where p = 9 (mod 16); and Z-cyclic directed moore (2,6) generalised whist tournament designs on p elements, where p = 7 (mod 12). In each of these cases, p is prime. In an effort to prove the existence of an infinite family of each of these tournaments, constructions are introduced and the conditions under which they give the initial round of a tournament of the kind we desire are found. A bound above which these conditions are always satisfied is then obtained, and we try to fill in the appropriate gaps below that bound. In Chapter 3 we investigate the existence of tournaments of the type seen in Chapter 2 which involve four players per game, with an additional property. This is known as the three person property and is defined in Chapter 1. Here, we focus on one of the constructions introduced in Chapter 2 for each type of tournament. Then we find a new bound using only that construction with the additional conditions introduced by the three person property, and again try to fill in the appropriate gaps below the bound. Chapter 4 is an investigation of logarithmic terraces and their properties. Very little work has been done on them previously, so this was really an opportunity to look at them more closely in an effort to find as many interesting properties as possible. Some general results and examples are given, with the focal point of the chapter being the study of terraces which are simultaneously logarithmic for two different primitive roots. In Chapter 5, a more specific problem is addressed which involves training schedules for athletes. Here we want n(n - 1) athletes to carry out n tasks in some order, then keep repeating them in different orders in blocks of n as many times as possible so that certain conditions are satisfied. These conditions are listed in Chapter 5. We make use of the Williams terrace and the Owens terrace in our attempt to find a general method which allows the given conditions to be satisfied and gets as close as possible to the theoretical limit where each athlete carries out the n tasks n - 1 times

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports

Algorithms for classification of combinatorial objects

A recurrently occurring problem in combinatorics is the need to completely characterize a finite set of finite objects implicitly defined by a set of constraints. For example, one could ask for a list of all possible ways to schedule a football tournament for twelve teams: every team is to play against every other team during an eleven-round tournament, such that every team plays exactly one game in every round. Such a characterization is called a classification for the objects of interest. Classification is typically conducted up to a notion of structural equivalence (isomorphism) between the objects. For example, one can view two tournament schedules as having the same structure if one can be obtained from the other by renaming the teams and reordering the rounds. This thesis examines algorithms for classification of combinatorial objects up to isomorphism. The thesis consists of five articles – each devoted to a specific family of objects – together with a summary surveying related research and emphasizing the underlying common concepts and techniques, such as backtrack search, isomorphism (viewed through group actions), symmetry, isomorph rejection, and computing isomorphism. From an algorithmic viewpoint the focus of the thesis is practical, with interest on algorithms that perform well in practice and yield new classification results; theoretical properties such as the asymptotic resource usage of the algorithms are not considered. The main result of this thesis is a classification of the Steiner triple systems of order 19. The other results obtained include the nonexistence of a resolvable 2-(15, 5, 4) design, a classification of the one-factorizations of k-regular graphs of order 12 for k ≤ 6 and k = 10, 11, a classification of the near-resolutions of 2-(13, 4, 3) designs together with the associated thirteen-player whist tournaments, and a classification of the Steiner triple systems of order 21 with a nontrivial automorphism group.reviewe

The Western Mistic, March 24, 1944

https://red.mnstate.edu/western-mistic/1380/thumbnail.jp

Energy efficiency with QoS control in dynamic optical networks with SDN enabled integrated control plane

© 2014 Elsevier B.V. All rights reserved. The paper presents energy efficient routing algorithms based on a novel integrated control plane platform. The centralized control plane structure enables the use of flexible heuristic algorithms for route selection in optical networks. Differentiated routing for various traffic types is used in our previous work. The work presented in this paper further optimizes the energy performance in the whole network by utilizing a multi-objective evolutionary algorithm for route selection. The trade-off between energy optimization and QoS for high priority traffic is examined and results show an overall improvement in energy performance whilst maintaining satisfactory QoS. Energy savings are obtained on the low priority traffic whilst the QoS for the high priority traffic is not degraded